Application of solid-phase concentration-dependent HSDM to the acid dye adsorption system

The fixed-bed adsorption of acid dyes onto granular activated carbon (Chemviron Filtrasorb 400) has been studied using a homogeneous surface diffusion model (HSDM). The model incorporates the external boundary layer mass transport and homogeneous diffusion inside the particle. A new orthogonal collocation method has been developed and used to solve the diffusion equations. This orthogonal collocation gives a faster solution method compared with the numerical Crank-Nicolson method. The surface diffusivity has been determined by an optimization procedure with minimization of sum of the error squared. The equilibrium relationship between the liquid-phase concentration and the solid-phase concentration has been described by the Redlich-Peterson isotherm. A solid-phase concentration-dependent surface diffusivity was introduced. The Darken model with the Redlich-Peterson isotherm was found to be a suitable correlation model for the adsorption of the acid dyes on carbon. The magnitude of the averaged D_s0 of each dye is in the order of AR114 > AB80 > AY117, which implies that, under the same solid-phase concentration gradient, the rate of mass transport diffusion is higher in AR114 than that in AB80 and AY117. This phenomenon may be explained by the different mobilities of the dye molecules present in the solution by the different arrangements of two sulfonic acid groups in the dye structures.